Finite Group Databasebeta

← Group #348352

Character table — Group #348352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444442244444444444488888888444444888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-111-1
χ101111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-1-11
χ111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-11-11
χ121111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-11-11-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-11111-1-1-1-1-1-111111111-1-1-1-11-1-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-11111-111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1111111-1-1-1-111-1-1-1-1111-11-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1111111-1-1-1-1-1-11111-1-1-11-11
χ172222222222-22-2-2-222222-2-20000000022222222-200-200-2-2-2-200000000000000000000
χ182222222222-22-2-2-222222-2-200000000-2-2-2-2-2-2-2-2-200-200222200000000000000000000
χ192222222222-22-2-2-22-2-2-2-2-2-2000000002222-2-2-2-2200200-2-22200000000000000000000
χ202222222222-22-2-2-22-2-2-2-2-2-200000000-2-2-2-2222220020022-2-200000000000000000000
χ2122222222-2-22-2222-222-2-2-2-22222-2-2-2-200000000-2222-2-2000000000000000000000000
χ2222222222-2-22-2222-222-2-2-2-2-2-2-2-2222200000000-2-2-2222000000000000000000000000
χ2322222222-2-22-2222-2-2-222-2-22222-2-2-2-2000000002-2-2-222000000000000000000000000
χ2422222222-2-22-2222-2-2-222-2-2-2-2-2-2222200000000222-2-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2220000000000000000200-20000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2220000000000000000200-2000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000000000000000-20020000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000000000000000-2002000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-222-2-2-22-20-200022-22-200000000002i2i−2i−2i2i2i−2i−2i000000000000000000i2−i22−2i2−i22−20000
χ3022-222-2-2-22-20-200022-22-200000000002i2i−2i−2i2i2i−2i−2i000000000000000000−i2i2−22−i2i2−220000
χ3122-222-2-2-22-20-200022-22-20000000000−2i−2i2i2i−2i−2i2i2i000000000000000000i2−i2−22i2−i2−220000
χ3222-222-2-2-22-20-200022-22-20000000000−2i−2i2i2i−2i−2i2i2i000000000000000000−i2i22−2−i2i22−20000
χ3322-222-2-2-22-20-20002-22-2200000000002i2i−2i−2i−2i−2i2i2i000000000000000000i2−i22−2−i2i2−220000
χ3422-222-2-2-22-20-20002-22-2200000000002i2i−2i−2i−2i−2i2i2i000000000000000000−i2i2−22i2−i22−20000
χ3522-222-2-2-22-20-20002-22-220000000000−2i−2i2i2i2i2i−2i−2i000000000000000000i2−i2−22−i2i22−20000
χ3622-222-2-2-22-20-20002-22-220000000000−2i−2i2i2i2i2i−2i−2i000000000000000000−i2i22−2i2−i2−220000
χ372-2-22-2-222222-2-2-22-200002-222-2-222-2-200002i−2i2i−2i000000002i−2i00002i−2i2i−2i000000000000
χ382-2-22-2-222222-2-2-22-200002-222-2-222-2-20000−2i2i−2i2i00000000−2i2i0000−2i2i−2i2i000000000000
χ392-2-22-2-222222-2-2-22-200002-2-2-222-2-22200002i−2i2i−2i000000002i−2i0000−2i2i−2i2i000000000000
χ402-2-22-2-222222-2-2-22-200002-2-2-222-2-2220000−2i2i−2i2i00000000−2i2i00002i−2i2i−2i000000000000
χ412-2-22-2-22222-2-222-2-20000-220000000000002i−2i2i−2i02-202-200−2i2i2i−2i2i−2i0000000000000000
χ422-2-22-2-22222-2-222-2-20000-220000000000002i−2i2i−2i0-220-2200−2i2i−2i2i−2i2i0000000000000000
χ432-2-22-2-22222-2-222-2-20000-22000000000000−2i2i−2i2i02-202-2002i−2i−2i2i−2i2i0000000000000000
χ442-2-22-2-22222-2-222-2-20000-22000000000000−2i2i−2i2i0-220-22002i−2i2i−2i2i−2i0000000000000000
χ452-2-22-2-222-2-222-2-2220000-2222-2-2-2-2222-22-200000000002-2002-2-220000000000000000
χ462-2-22-2-222-2-222-2-2220000-2222-2-2-2-222-22-220000000000-2200-222-20000000000000000
χ472-2-22-2-222-2-222-2-2220000-22-2-22222-2-22-22-200000000002-200-222-20000000000000000
χ482-2-22-2-222-2-222-2-2220000-22-2-22222-2-2-22-220000000000-22002-2-220000000000000000
χ492-2-22-2-222-2-2-2222-2200002-2000000002-22-2000002-20-22-220000002-2-22000000000000
χ502-2-22-2-222-2-2-2222-2200002-2000000002-22-200000-2202-2-22000000-222-2000000000000
χ512-2-22-2-222-2-2-2222-2200002-200000000-22-22000002-20-222-2000000-222-2000000000000
χ522-2-22-2-222-2-2-2222-2200002-200000000-22-2200000-2202-22-20000002-2-22000000000000
χ5344-444-4-4-4-4404000-44-4-44000000000000000000000000000000000000000000000000
χ5444-444-4-4-4-4404000-4-444-4000000000000000000000000000000000000000000000000
χ5544-4-4-44-4400404-4-400000004i−4i4i−4i000000000000000000000000000000000000000000
χ5644-4-4-44-4400404-4-40000000−4i4i−4i4i000000000000000000000000000000000000000000
χ5744-4-4-44-4400-40-444000000000004-44-400000000000000000000000000000000000000
χ5844-4-4-44-4400-40-44400000000000-44-4400000000000000000000000000000000000000
χ594-444-44-4-44-404000-40000000000000000004-4-44000000000000000000000000000000
χ604-444-44-4-44-404000-4000000000000000000-444-4000000000000000000000000000000
χ614-444-44-4-4-440-40004000000000000004i−4i−4i4i0000000000000000000000000000000000
χ624-444-44-4-4-440-4000400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ634-44-44-4-440040-44-400000004i−4i−4i4i000000000000000000000000000000000000000000
χ644-44-44-4-440040-44-40000000−4i4i4i−4i000000000000000000000000000000000000000000
χ654-44-44-4-4400-404-44000000000004-4-4400000000000000000000000000000000000000
χ664-44-44-4-4400-404-4400000000000-444-400000000000000000000000000000000000000
χ67888-8-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).